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 ArcTanh

 http://functions.wolfram.com/01.27.27.3316.01

 Input Form

 ArcTanh[1/Sqrt[1 - z]] == (Pi I)/2 + ArcSech[Sqrt[z]] /; Inequality[0, Less, Arg[z], LessEqual, Pi]

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox[RowBox[List["1", "-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List["ArcSech", "[", SqrtBox["z"], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

 MathML Form

 tanh - 1 ( 1 1 - z ) π 2 + sech - 1 ( z ) /; 0 < arg ( z ) π Condition 1 1 -1 z 1 2 -1 2 -1 z 1 2 Inequality 0 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox[RowBox[List["1", "-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List["ArcSech", "[", SqrtBox["z"], "]"]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2003-08-21